Autoencoders¶
Autoencoders are a useful tool as a dimension reduction technique.
- The input is first
compresseddown to a few neurons (bottleneck) - this is the encoder part - Then the compressed data is
decompressedto be as close to the original input as possible (based on a loss function) - this is the decoder part
Important properties:
- compression is learned automatically by the neural network, no need for hand-crafted compression techniques
- the compression is not lossless, we always lose some information in the process
- compression is learned from the samples, thus will be specific to the training data
In [3]:
#import tensorflow as tf
#tf.config.set_visible_devices([], "GPU")
In [4]:
from IPython.display import Image
Image("autoencoder.png")
Out[4]:
Load the MNIST dataset (don't forget to rescale the pixel intensities!)¶
In [75]:
from keras.datasets import mnist
(X_train, y_train), (X_test, y_test) = mnist.load_data()
X_train = X_train / 255
X_test = X_test / 255
X_train = X_train.reshape(-1, 784)
X_test = X_test.reshape(-1, 784)
X_train.shape, X_test.shape
Out[75]:
((60000, 784), (10000, 784))
Simplest autoencoder: one single hidden layer with 2 neurons and linear activation on the first layer¶
In [8]:
from keras.regularizers import L2
from keras.optimizers import SGD, Adam, RMSprop
from keras.layers import Add, Input, Conv2D, ZeroPadding2D, MaxPooling2D, Flatten, Dropout, Dense, Activation, GlobalAveragePooling2D, BatchNormalization, Reshape
from keras.models import Sequential, Model
from keras.utils import plot_model
import numpy as np
# Build the model with Functional model building
inp = Input(shape=(784, ))
encoder = Dense(2, activation="linear")(inp)
decoder = Dense(784, activation="sigmoid")(encoder) # don't use SOFTMAX!
model = Model(inputs=inp, outputs=decoder)
model.summary()
Model: "functional"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer (InputLayer) │ (None, 784) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense (Dense) │ (None, 2) │ 1,570 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 784) │ 2,352 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 3,922 (15.32 KB)
Trainable params: 3,922 (15.32 KB)
Non-trainable params: 0 (0.00 B)
Reshape the train and test matrices, then compile and train the model¶
- in
model.fit()we needX_traintwice: as input features and as true labels for loss calculation, too - we can use
(X_test, X_test)for validation data
In [10]:
0.055**0.5
Out[10]:
0.2345207879911715
In [9]:
model.compile(loss="mean_squared_error",
optimizer=Adam())
# don't use categorical_crossentropy, another good choice would have been "binary_crossentropy"
train = model.fit(X_train, X_train,
epochs=30,
batch_size=32,
verbose=1,
validation_data=(X_test, X_test))
Epoch 1/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 333us/step - loss: 0.0885 - val_loss: 0.0603 Epoch 2/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 311us/step - loss: 0.0595 - val_loss: 0.0582 Epoch 3/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 315us/step - loss: 0.0579 - val_loss: 0.0572 Epoch 4/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 314us/step - loss: 0.0571 - val_loss: 0.0567 Epoch 5/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 314us/step - loss: 0.0567 - val_loss: 0.0564 Epoch 6/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 315us/step - loss: 0.0564 - val_loss: 0.0562 Epoch 7/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 317us/step - loss: 0.0562 - val_loss: 0.0560 Epoch 8/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 318us/step - loss: 0.0561 - val_loss: 0.0558 Epoch 9/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 329us/step - loss: 0.0560 - val_loss: 0.0557 Epoch 10/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 326us/step - loss: 0.0559 - val_loss: 0.0556 Epoch 11/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 329us/step - loss: 0.0557 - val_loss: 0.0555 Epoch 12/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 319us/step - loss: 0.0555 - val_loss: 0.0554 Epoch 13/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 319us/step - loss: 0.0555 - val_loss: 0.0554 Epoch 14/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 319us/step - loss: 0.0556 - val_loss: 0.0553 Epoch 15/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 319us/step - loss: 0.0556 - val_loss: 0.0552 Epoch 16/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 322us/step - loss: 0.0554 - val_loss: 0.0551 Epoch 17/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 319us/step - loss: 0.0552 - val_loss: 0.0551 Epoch 18/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 320us/step - loss: 0.0553 - val_loss: 0.0550 Epoch 19/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 321us/step - loss: 0.0552 - val_loss: 0.0550 Epoch 20/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 322us/step - loss: 0.0554 - val_loss: 0.0550 Epoch 21/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 321us/step - loss: 0.0552 - val_loss: 0.0550 Epoch 22/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 322us/step - loss: 0.0553 - val_loss: 0.0550 Epoch 23/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 322us/step - loss: 0.0553 - val_loss: 0.0550 Epoch 24/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 320us/step - loss: 0.0553 - val_loss: 0.0550 Epoch 25/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 321us/step - loss: 0.0553 - val_loss: 0.0549 Epoch 26/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 323us/step - loss: 0.0553 - val_loss: 0.0550 Epoch 27/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 321us/step - loss: 0.0552 - val_loss: 0.0550 Epoch 28/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 333us/step - loss: 0.0553 - val_loss: 0.0549 Epoch 29/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 320us/step - loss: 0.0551 - val_loss: 0.0550 Epoch 30/30 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 1s 321us/step - loss: 0.0553 - val_loss: 0.0549
In [14]:
import matplotlib.pyplot as plt
%matplotlib inline
def plot_train(train):
plt.figure(figsize=(9, 6))
plt.plot(np.array(train.history['loss'])**0.5, 'r-', label='train')
plt.plot(np.array(train.history['val_loss'])**0.5, 'b-', label='validation')
plt.title("Root mean squared error")
plt.legend()
plt.show()
plot_train(train)
Let's plot a few test samples and their representations by the autoencoder¶
In [28]:
import matplotlib.pyplot as plt
for idx in range(10):
original_image = X_test[idx].reshape(28, 28)
fig, ax = plt.subplots(1, 2, figsize=(16, 6))
ax[0].imshow(original_image, cmap="gray")
ax[0].set_title("Original")
prediction = model.predict(X_test[idx].reshape(1, 784), verbose=0)
ax[1].imshow(prediction.reshape(28, 28), cmap="gray")
ax[1].set_title("Reconstructed")
Visualization with autoencoders¶
Since we reduced the number of features to , we can use this as a visualization tool, similarly to t-SNE. However, in general t-SNE is more effective in such visualizations.
In [29]:
encoder_model = Model(inputs=inp, outputs=encoder)
encoder_model.summary()
Model: "functional_1"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer (InputLayer) │ (None, 784) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense (Dense) │ (None, 2) │ 1,570 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 1,570 (6.13 KB)
Trainable params: 1,570 (6.13 KB)
Non-trainable params: 0 (0.00 B)
In [32]:
X_test_embedded = encoder_model.predict(X_test)
X_test_embedded
313/313 ━━━━━━━━━━━━━━━━━━━━ 0s 193us/step
Out[32]:
array([[-9.699953 , 7.0246954 ],
[-0.24602032, -2.0697458 ],
[-6.666047 , -5.270087 ],
...,
[-6.5780993 , 6.267766 ],
[-4.481531 , 2.978798 ],
[ 1.6271992 , 9.4660845 ]], dtype=float32)
In [38]:
import seaborn as sns
sns.scatterplot(x=X_test_embedded[:, 0],
y=X_test_embedded[:, 1],
hue=y_test,
palette="tab10",
alpha=0.5)
Out[38]:
<Axes: >
Let's do a t-SNE visualization just for comparison¶
In [39]:
from sklearn.manifold import TSNE
tsne = TSNE(n_components=2, random_state=42)
X_test_embedded = tsne.fit_transform(X_test)
X_test_embedded.shape
Out[39]:
(10000, 2)
In [40]:
sns.scatterplot(x=X_test_embedded[:, 0],
y=X_test_embedded[:, 1],
hue=y_test,
palette="tab10",
alpha=0.5)
Out[40]:
<Axes: >
Let's do this with more hidden neurons¶
In [41]:
from keras.callbacks import EarlyStopping
def create_autoencoder(n_hidden, epochs=100, batch_size=512, activation="relu"):
inp = Input(shape=(784, ))
encoder = Dense(n_hidden, activation=activation)(inp)
decoder = Dense(784, activation="sigmoid")(encoder) # don't use SOFTMAX!
model = Model(inputs=inp, outputs=decoder)
model.summary()
model.compile(loss="mean_squared_error",
optimizer=Adam())
# don't use categorical_crossentropy, another good choice would have been "binary_crossentropy"
early_stop = EarlyStopping(patience=5, monitor="val_loss", mode="min")
train = model.fit(X_train, X_train,
epochs=epochs,
batch_size=batch_size,
verbose=1,
callbacks=[early_stop],
validation_split=0.1)
return model, train
In [42]:
model, train = create_autoencoder(n_hidden=10, epochs=100, batch_size=32, activation="relu")
Model: "functional_2"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_1 (InputLayer) │ (None, 784) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 10) │ 7,850 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 784) │ 8,624 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 16,474 (64.35 KB)
Trainable params: 16,474 (64.35 KB)
Non-trainable params: 0 (0.00 B)
Epoch 1/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 397us/step - loss: 0.0704 - val_loss: 0.0345 Epoch 2/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 382us/step - loss: 0.0342 - val_loss: 0.0326 Epoch 3/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 378us/step - loss: 0.0325 - val_loss: 0.0315 Epoch 4/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 377us/step - loss: 0.0314 - val_loss: 0.0308 Epoch 5/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 400us/step - loss: 0.0310 - val_loss: 0.0306 Epoch 6/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 381us/step - loss: 0.0306 - val_loss: 0.0302 Epoch 7/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 391us/step - loss: 0.0304 - val_loss: 0.0302 Epoch 8/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 411us/step - loss: 0.0303 - val_loss: 0.0300 Epoch 9/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 414us/step - loss: 0.0302 - val_loss: 0.0300 Epoch 10/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 396us/step - loss: 0.0301 - val_loss: 0.0299 Epoch 11/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 373us/step - loss: 0.0301 - val_loss: 0.0299 Epoch 12/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 376us/step - loss: 0.0300 - val_loss: 0.0298 Epoch 13/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 370us/step - loss: 0.0300 - val_loss: 0.0298 Epoch 14/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 368us/step - loss: 0.0300 - val_loss: 0.0298 Epoch 15/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 383us/step - loss: 0.0298 - val_loss: 0.0298 Epoch 16/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 398us/step - loss: 0.0298 - val_loss: 0.0297 Epoch 17/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 391us/step - loss: 0.0298 - val_loss: 0.0298 Epoch 18/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 396us/step - loss: 0.0298 - val_loss: 0.0297 Epoch 19/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 383us/step - loss: 0.0298 - val_loss: 0.0297 Epoch 20/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 401us/step - loss: 0.0298 - val_loss: 0.0297 Epoch 21/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 390us/step - loss: 0.0298 - val_loss: 0.0297 Epoch 22/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 391us/step - loss: 0.0298 - val_loss: 0.0296 Epoch 23/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 390us/step - loss: 0.0297 - val_loss: 0.0297 Epoch 24/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 380us/step - loss: 0.0297 - val_loss: 0.0296 Epoch 25/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 373us/step - loss: 0.0298 - val_loss: 0.0296 Epoch 26/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 372us/step - loss: 0.0297 - val_loss: 0.0296 Epoch 27/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 383us/step - loss: 0.0297 - val_loss: 0.0296 Epoch 28/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 400us/step - loss: 0.0296 - val_loss: 0.0296 Epoch 29/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 388us/step - loss: 0.0297 - val_loss: 0.0296 Epoch 30/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 428us/step - loss: 0.0296 - val_loss: 0.0296 Epoch 31/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 430us/step - loss: 0.0297 - val_loss: 0.0297 Epoch 32/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 428us/step - loss: 0.0296 - val_loss: 0.0296 Epoch 33/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 400us/step - loss: 0.0296 - val_loss: 0.0296 Epoch 34/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 392us/step - loss: 0.0297 - val_loss: 0.0295 Epoch 35/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 393us/step - loss: 0.0295 - val_loss: 0.0295 Epoch 36/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 388us/step - loss: 0.0296 - val_loss: 0.0295 Epoch 37/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 391us/step - loss: 0.0295 - val_loss: 0.0296 Epoch 38/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 395us/step - loss: 0.0296 - val_loss: 0.0295 Epoch 39/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 391us/step - loss: 0.0295 - val_loss: 0.0295 Epoch 40/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 418us/step - loss: 0.0296 - val_loss: 0.0296
In [43]:
for idx in range(10):
original_image = X_test[idx].reshape(28, 28)
fig, ax = plt.subplots(1, 2, figsize=(16, 6))
ax[0].imshow(original_image, cmap="gray")
ax[0].set_title("Original")
prediction = model.predict(X_test[idx].reshape(1, 784), verbose=0)
ax[1].imshow(prediction.reshape(28, 28), cmap="gray")
ax[1].set_title("Reconstructed")
Number of hidden neurons = 5¶
In [44]:
model, train = create_autoencoder(n_hidden=5, epochs=100, batch_size=32, activation="relu")
for idx in range(10):
original_image = X_test[idx].reshape(28, 28)
fig, ax = plt.subplots(1, 2, figsize=(16, 6))
ax[0].imshow(original_image, cmap="gray")
ax[0].set_title("Original")
prediction = model.predict(X_test[idx].reshape(1, 784), verbose=0)
ax[1].imshow(prediction.reshape(28, 28), cmap="gray")
ax[1].set_title("Reconstructed")
Model: "functional_3"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_2 (InputLayer) │ (None, 784) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_4 (Dense) │ (None, 5) │ 3,925 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_5 (Dense) │ (None, 784) │ 4,704 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 8,629 (33.71 KB)
Trainable params: 8,629 (33.71 KB)
Non-trainable params: 0 (0.00 B)
Epoch 1/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 381us/step - loss: 0.0810 - val_loss: 0.0474 Epoch 2/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 373us/step - loss: 0.0465 - val_loss: 0.0442 Epoch 3/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 358us/step - loss: 0.0444 - val_loss: 0.0433 Epoch 4/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 359us/step - loss: 0.0435 - val_loss: 0.0428 Epoch 5/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 365us/step - loss: 0.0431 - val_loss: 0.0426 Epoch 6/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 346us/step - loss: 0.0429 - val_loss: 0.0424 Epoch 7/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 363us/step - loss: 0.0427 - val_loss: 0.0424 Epoch 8/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 352us/step - loss: 0.0426 - val_loss: 0.0423 Epoch 9/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 348us/step - loss: 0.0425 - val_loss: 0.0423 Epoch 10/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 346us/step - loss: 0.0425 - val_loss: 0.0423 Epoch 11/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 351us/step - loss: 0.0424 - val_loss: 0.0423 Epoch 12/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 352us/step - loss: 0.0424 - val_loss: 0.0421 Epoch 13/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 351us/step - loss: 0.0423 - val_loss: 0.0421 Epoch 14/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 349us/step - loss: 0.0423 - val_loss: 0.0421 Epoch 15/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 363us/step - loss: 0.0424 - val_loss: 0.0420 Epoch 16/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 353us/step - loss: 0.0423 - val_loss: 0.0420 Epoch 17/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 364us/step - loss: 0.0422 - val_loss: 0.0421 Epoch 18/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 362us/step - loss: 0.0424 - val_loss: 0.0420 Epoch 19/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 351us/step - loss: 0.0423 - val_loss: 0.0420 Epoch 20/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 384us/step - loss: 0.0424 - val_loss: 0.0420 Epoch 21/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 372us/step - loss: 0.0423 - val_loss: 0.0419 Epoch 22/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 365us/step - loss: 0.0422 - val_loss: 0.0419 Epoch 23/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 369us/step - loss: 0.0422 - val_loss: 0.0419 Epoch 24/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 371us/step - loss: 0.0422 - val_loss: 0.0419 Epoch 25/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 365us/step - loss: 0.0423 - val_loss: 0.0419 Epoch 26/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 376us/step - loss: 0.0421 - val_loss: 0.0419 Epoch 27/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 377us/step - loss: 0.0421 - val_loss: 0.0418 Epoch 28/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 373us/step - loss: 0.0422 - val_loss: 0.0419 Epoch 29/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 379us/step - loss: 0.0421 - val_loss: 0.0419 Epoch 30/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 368us/step - loss: 0.0422 - val_loss: 0.0419 Epoch 31/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 359us/step - loss: 0.0422 - val_loss: 0.0419 Epoch 32/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 363us/step - loss: 0.0422 - val_loss: 0.0418 Epoch 33/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 360us/step - loss: 0.0422 - val_loss: 0.0418 Epoch 34/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 346us/step - loss: 0.0422 - val_loss: 0.0418 Epoch 35/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 357us/step - loss: 0.0420 - val_loss: 0.0418 Epoch 36/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 348us/step - loss: 0.0422 - val_loss: 0.0418 Epoch 37/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 356us/step - loss: 0.0421 - val_loss: 0.0417 Epoch 38/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 357us/step - loss: 0.0421 - val_loss: 0.0418 Epoch 39/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 362us/step - loss: 0.0420 - val_loss: 0.0418 Epoch 40/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 362us/step - loss: 0.0420 - val_loss: 0.0418 Epoch 41/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 365us/step - loss: 0.0421 - val_loss: 0.0418 Epoch 42/100 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 1s 363us/step - loss: 0.0422 - val_loss: 0.0418
With one single layer and linear activations we usually end up with good approximations to the PCA (principal component analysis) embeddings.
Autoencoders with Convolutional neural networks¶
- we use Conv2D and MaxPooling2D layers in the encoder part to reduce the size to (4, 4, 8)
- the bottleneck consists of neurons
- the decoder layers needs Conv2D and UpSampling2D layers (upsampling = repeating rows/columns to increase the dimension)
In [74]:
from keras.layers import UpSampling2D
inp = Input(shape=(28, 28, 1))
conv1 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(inp)
pool1 = MaxPooling2D(2)(conv1)
conv2 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(pool1)
pool2 = MaxPooling2D(2)(conv2)
conv3 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(pool2)
up1 = UpSampling2D(2)(conv3)
conv4 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(up1)
up2 = UpSampling2D(2)(conv4)
conv5 = Conv2D(filters=1, kernel_size=(3, 3), activation="sigmoid", padding="same")(up2)
model = Model(inputs=inp, outputs=conv5)
model.summary()
Model: "functional_12"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_13 (InputLayer) │ (None, 28, 28, 1) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_32 (Conv2D) │ (None, 28, 28, 8) │ 80 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ max_pooling2d_15 (MaxPooling2D) │ (None, 14, 14, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_33 (Conv2D) │ (None, 14, 14, 8) │ 584 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ max_pooling2d_16 (MaxPooling2D) │ (None, 7, 7, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_34 (Conv2D) │ (None, 7, 7, 8) │ 584 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ up_sampling2d_11 (UpSampling2D) │ (None, 14, 14, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_35 (Conv2D) │ (None, 14, 14, 8) │ 584 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ up_sampling2d_12 (UpSampling2D) │ (None, 28, 28, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_36 (Conv2D) │ (None, 28, 28, 1) │ 73 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 1,905 (7.44 KB)
Trainable params: 1,905 (7.44 KB)
Non-trainable params: 0 (0.00 B)
Let's reload the data, because we need the original tensors¶
In [79]:
(X_train, y_train), (X_test, y_test) = mnist.load_data()
X_train = X_train.reshape(-1, 28, 28, 1)
X_test = X_test.reshape(-1, 28, 28, 1)
model.compile(loss="mean_squared_error",
optimizer=Adam())
# don't use categorical_crossentropy, another good choice would have been "binary_crossentropy"
early_stop = EarlyStopping(patience=5, monitor="val_loss", mode="min")
train = model.fit(X_train, X_train,
epochs=10,
batch_size=32,
verbose=1,
callbacks=[early_stop],
validation_split=0.1)
Epoch 1/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7220.3760 - val_loss: 7180.2700 Epoch 2/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7235.2388 - val_loss: 7180.2598 Epoch 3/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7212.6484 - val_loss: 7180.2534 Epoch 4/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7223.3521 - val_loss: 7180.2451 Epoch 5/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7211.6426 - val_loss: 7180.2441 Epoch 6/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7209.0469 - val_loss: 7180.2422 Epoch 7/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7208.7236 - val_loss: 7180.2354 Epoch 8/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7230.2012 - val_loss: 7180.2446 Epoch 9/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7212.3408 - val_loss: 7180.2407 Epoch 10/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 7211.9336 - val_loss: 7180.2334
Plot the original and reconstructed images¶
In [80]:
for idx in range(10):
original_image = X_test[idx].reshape(28, 28)
fig, ax = plt.subplots(1, 2, figsize=(16, 6))
ax[0].imshow(original_image, cmap="gray")
ax[0].set_title("Original")
prediction = model.predict(X_test[idx].reshape(1, 28, 28, 1), verbose=0)
ax[1].imshow(prediction.reshape(28, 28), cmap="gray")
ax[1].set_title("Reconstructed")
In [81]:
(X_train, y_train), (X_test, y_test) = mnist.load_data()
X_train = X_train.reshape(-1, 28, 28, 1) / 255
X_test = X_test.reshape(-1, 28, 28, 1) / 255 # Don't forget to rescale!!
model.compile(loss="mean_squared_error",
optimizer=Adam())
# don't use categorical_crossentropy, another good choice would have been "binary_crossentropy"
early_stop = EarlyStopping(patience=5, monitor="val_loss", mode="min")
train = model.fit(X_train, X_train,
epochs=10,
batch_size=32,
verbose=1,
callbacks=[early_stop],
validation_split=0.1)
for idx in range(10):
original_image = X_test[idx].reshape(28, 28)
fig, ax = plt.subplots(1, 2, figsize=(16, 6))
ax[0].imshow(original_image, cmap="gray")
ax[0].set_title("Original")
prediction = model.predict(X_test[idx].reshape(1, 28, 28, 1), verbose=0)
ax[1].imshow(prediction.reshape(28, 28), cmap="gray")
ax[1].set_title("Reconstructed")
Epoch 1/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.1119 - val_loss: 0.1114 Epoch 2/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1122 - val_loss: 0.1114 Epoch 3/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 6ms/step - loss: 0.1121 - val_loss: 0.1114 Epoch 4/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 6ms/step - loss: 0.1122 - val_loss: 0.1114 Epoch 5/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1121 - val_loss: 0.1114 Epoch 6/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.1120 - val_loss: 0.1114
Change the loss function to binary_crossentropy to enforce larger penalties¶
In [82]:
(X_train, y_train), (X_test, y_test) = mnist.load_data()
X_train = X_train.reshape(-1, 28, 28, 1) / 255
X_test = X_test.reshape(-1, 28, 28, 1) / 255 # Don't forget to rescale!!
model.compile(loss="binary_crossentropy",
metrics=["mean_squared_error"],
optimizer=Adam())
# don't use categorical_crossentropy, another good choice would have been "binary_crossentropy"
early_stop = EarlyStopping(patience=5, monitor="val_loss", mode="min")
train = model.fit(X_train, X_train,
epochs=10,
batch_size=32,
verbose=1,
callbacks=[early_stop],
validation_split=0.1)
for idx in range(10):
original_image = X_test[idx].reshape(28, 28)
fig, ax = plt.subplots(1, 2, figsize=(16, 6))
ax[0].imshow(original_image, cmap="gray")
ax[0].set_title("Original")
prediction = model.predict(X_test[idx].reshape(1, 28, 28, 1), verbose=0)
ax[1].imshow(prediction.reshape(28, 28), cmap="gray")
ax[1].set_title("Reconstructed")
Epoch 1/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 5ms/step - loss: 0.3457 - mean_squared_error: 0.0236 - val_loss: 0.0888 - val_mean_squared_error: 0.0089 Epoch 2/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 6ms/step - loss: 0.0858 - mean_squared_error: 0.0080 - val_loss: 0.0819 - val_mean_squared_error: 0.0067 Epoch 3/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 6ms/step - loss: 0.0802 - mean_squared_error: 0.0062 - val_loss: 0.0784 - val_mean_squared_error: 0.0056 Epoch 4/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0774 - mean_squared_error: 0.0053 - val_loss: 0.0764 - val_mean_squared_error: 0.0049 Epoch 5/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0755 - mean_squared_error: 0.0047 - val_loss: 0.0751 - val_mean_squared_error: 0.0045 Epoch 6/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0742 - mean_squared_error: 0.0044 - val_loss: 0.0743 - val_mean_squared_error: 0.0043 Epoch 7/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0737 - mean_squared_error: 0.0042 - val_loss: 0.0738 - val_mean_squared_error: 0.0041 Epoch 8/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0730 - mean_squared_error: 0.0040 - val_loss: 0.0734 - val_mean_squared_error: 0.0040 Epoch 9/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0726 - mean_squared_error: 0.0039 - val_loss: 0.0731 - val_mean_squared_error: 0.0039 Epoch 10/10 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0724 - mean_squared_error: 0.0039 - val_loss: 0.0729 - val_mean_squared_error: 0.0039
Denoising images with autoencoders¶
We can use autoencoders to remove noise from images by training to construct clean images from noisy ones.
We start by adding random noise to train and test images.
In [97]:
(X_train, y_train), (X_test, y_test) = mnist.load_data()
X_train = X_train.reshape(-1, 28, 28, 1) / 255
X_test = X_test.reshape(-1, 28, 28, 1) / 255 # Don't forget to rescale!!
rs = np.random.RandomState(42)
factor = 1
X_train_noisy = X_train + factor * rs.random(size=X_train.shape)
X_test_noisy = X_test + factor * rs.random(size=X_test.shape)
for idx in range(10):
fig, ax = plt.subplots(1, 2, figsize=(16, 6))
ax[0].imshow(X_train_noisy[idx].reshape(28, 28), cmap="gray")
ax[1].imshow(X_train[idx].reshape(28, 28), cmap="gray")
Let's create the autoencoder with Conv2D, MaxPooling2D and UpSampling2D layers¶
In [98]:
inp = Input(shape=(28, 28, 1))
conv1 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(inp)
pool1 = MaxPooling2D(2)(conv1)
conv2 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(pool1)
pool2 = MaxPooling2D(2)(conv2)
conv3 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(pool2)
up1 = UpSampling2D(2)(conv3)
conv4 = Conv2D(filters=8, kernel_size=(3, 3), activation="relu", padding="same")(up1)
up2 = UpSampling2D(2)(conv4)
conv5 = Conv2D(filters=1, kernel_size=(3, 3), activation="sigmoid", padding="same")(up2)
model = Model(inputs=inp, outputs=conv5)
model.summary()
Model: "functional_13"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_14 (InputLayer) │ (None, 28, 28, 1) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_37 (Conv2D) │ (None, 28, 28, 8) │ 80 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ max_pooling2d_17 (MaxPooling2D) │ (None, 14, 14, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_38 (Conv2D) │ (None, 14, 14, 8) │ 584 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ max_pooling2d_18 (MaxPooling2D) │ (None, 7, 7, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_39 (Conv2D) │ (None, 7, 7, 8) │ 584 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ up_sampling2d_13 (UpSampling2D) │ (None, 14, 14, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_40 (Conv2D) │ (None, 14, 14, 8) │ 584 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ up_sampling2d_14 (UpSampling2D) │ (None, 28, 28, 8) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ conv2d_41 (Conv2D) │ (None, 28, 28, 1) │ 73 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 1,905 (7.44 KB)
Trainable params: 1,905 (7.44 KB)
Non-trainable params: 0 (0.00 B)
In [100]:
model.compile(loss="binary_crossentropy",
metrics=["mean_squared_error"],
optimizer=Adam())
early_stop = EarlyStopping(patience=5, monitor="val_loss", mode="min")
model.fit(X_train_noisy, X_train,
epochs=30,
batch_size=32,
verbose=1,
validation_split=0.1,
callbacks=[early_stop])
Epoch 1/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0935 - mean_squared_error: 0.0104 - val_loss: 0.0935 - val_mean_squared_error: 0.0102 Epoch 2/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0925 - mean_squared_error: 0.0100 - val_loss: 0.0923 - val_mean_squared_error: 0.0098 Epoch 3/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0919 - mean_squared_error: 0.0098 - val_loss: 0.0914 - val_mean_squared_error: 0.0096 Epoch 4/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0908 - mean_squared_error: 0.0095 - val_loss: 0.0910 - val_mean_squared_error: 0.0095 Epoch 5/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0904 - mean_squared_error: 0.0094 - val_loss: 0.0904 - val_mean_squared_error: 0.0092 Epoch 6/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0897 - mean_squared_error: 0.0092 - val_loss: 0.0900 - val_mean_squared_error: 0.0092 Epoch 7/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0892 - mean_squared_error: 0.0090 - val_loss: 0.0909 - val_mean_squared_error: 0.0095 Epoch 8/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0888 - mean_squared_error: 0.0088 - val_loss: 0.0893 - val_mean_squared_error: 0.0089 Epoch 9/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0883 - mean_squared_error: 0.0087 - val_loss: 0.0893 - val_mean_squared_error: 0.0089 Epoch 10/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0879 - mean_squared_error: 0.0086 - val_loss: 0.0883 - val_mean_squared_error: 0.0086 Epoch 11/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0875 - mean_squared_error: 0.0085 - val_loss: 0.0883 - val_mean_squared_error: 0.0086 Epoch 12/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0873 - mean_squared_error: 0.0084 - val_loss: 0.0881 - val_mean_squared_error: 0.0085 Epoch 13/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0873 - mean_squared_error: 0.0083 - val_loss: 0.0877 - val_mean_squared_error: 0.0084 Epoch 14/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0869 - mean_squared_error: 0.0082 - val_loss: 0.0873 - val_mean_squared_error: 0.0083 Epoch 15/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0866 - mean_squared_error: 0.0082 - val_loss: 0.0873 - val_mean_squared_error: 0.0083 Epoch 16/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0864 - mean_squared_error: 0.0081 - val_loss: 0.0871 - val_mean_squared_error: 0.0082 Epoch 17/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0865 - mean_squared_error: 0.0081 - val_loss: 0.0871 - val_mean_squared_error: 0.0082 Epoch 18/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0859 - mean_squared_error: 0.0080 - val_loss: 0.0868 - val_mean_squared_error: 0.0081 Epoch 19/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0860 - mean_squared_error: 0.0080 - val_loss: 0.0868 - val_mean_squared_error: 0.0081 Epoch 20/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0860 - mean_squared_error: 0.0079 - val_loss: 0.0864 - val_mean_squared_error: 0.0079 Epoch 21/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0859 - mean_squared_error: 0.0079 - val_loss: 0.0863 - val_mean_squared_error: 0.0080 Epoch 22/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0858 - mean_squared_error: 0.0079 - val_loss: 0.0862 - val_mean_squared_error: 0.0079 Epoch 23/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0857 - mean_squared_error: 0.0078 - val_loss: 0.0862 - val_mean_squared_error: 0.0079 Epoch 24/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0855 - mean_squared_error: 0.0078 - val_loss: 0.0860 - val_mean_squared_error: 0.0078 Epoch 25/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0855 - mean_squared_error: 0.0078 - val_loss: 0.0856 - val_mean_squared_error: 0.0077 Epoch 26/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0847 - mean_squared_error: 0.0075 - val_loss: 0.0850 - val_mean_squared_error: 0.0075 Epoch 27/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0842 - mean_squared_error: 0.0074 - val_loss: 0.0846 - val_mean_squared_error: 0.0074 Epoch 28/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0841 - mean_squared_error: 0.0073 - val_loss: 0.0845 - val_mean_squared_error: 0.0074 Epoch 29/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0836 - mean_squared_error: 0.0072 - val_loss: 0.0845 - val_mean_squared_error: 0.0074 Epoch 30/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.0838 - mean_squared_error: 0.0072 - val_loss: 0.0843 - val_mean_squared_error: 0.0073
Out[100]:
<keras.src.callbacks.history.History at 0x3afcd3950>
Plot the noisy, the reconstructed and the original images¶
In [107]:
for idx in range(10):
fig, ax = plt.subplots(1, 3, figsize=(18, 6))
ax[0].set_title("Noisy")
ax[1].set_title("Original")
ax[2].set_title("Reconstructed")
ax[0].imshow(X_test_noisy[idx].reshape(28, 28), cmap="gray")
ax[1].imshow(X_test[idx].reshape(28, 28), cmap="gray")
prediction = model.predict(X_test_noisy[idx].reshape(1, 28, 28, 1), verbose=0)
ax[2].imshow(prediction.reshape(28, 28), cmap="gray")
Increase the noise - No re-training here!¶
In [109]:
factor = 2
X_train_noisy2 = X_train + factor * rs.random(size=X_train.shape)
X_test_noisy2 = X_test + factor * rs.random(size=X_test.shape)
for idx in range(10):
fig, ax = plt.subplots(1, 3, figsize=(18, 6))
ax[0].set_title("Noisy")
ax[1].set_title("Original")
ax[2].set_title("Reconstructed")
ax[0].imshow(X_test_noisy2[idx].reshape(28, 28), cmap="gray")
ax[1].imshow(X_test[idx].reshape(28, 28), cmap="gray")
prediction = model.predict(X_test_noisy2[idx].reshape(1, 28, 28, 1), verbose=0)
ax[2].imshow(prediction.reshape(28, 28), cmap="gray")
Re-train the model with larger noise¶
In [110]:
model.compile(loss="binary_crossentropy",
metrics=["mean_squared_error"],
optimizer=Adam())
early_stop = EarlyStopping(patience=5, monitor="val_loss", mode="min")
model.fit(X_train_noisy2, X_train,
epochs=30,
batch_size=32,
verbose=1,
validation_split=0.1,
callbacks=[early_stop])
for idx in range(10):
fig, ax = plt.subplots(1, 3, figsize=(18, 6))
ax[0].set_title("Noisy")
ax[1].set_title("Original")
ax[2].set_title("Reconstructed")
ax[0].imshow(X_test_noisy2[idx].reshape(28, 28), cmap="gray")
ax[1].imshow(X_test[idx].reshape(28, 28), cmap="gray")
prediction = model.predict(X_test_noisy2[idx].reshape(1, 28, 28, 1), verbose=0)
ax[2].imshow(prediction.reshape(28, 28), cmap="gray")
Epoch 1/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1325 - mean_squared_error: 0.0217 - val_loss: 0.1097 - val_mean_squared_error: 0.0152 Epoch 2/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1089 - mean_squared_error: 0.0150 - val_loss: 0.1086 - val_mean_squared_error: 0.0148 Epoch 3/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1082 - mean_squared_error: 0.0148 - val_loss: 0.1085 - val_mean_squared_error: 0.0148 Epoch 4/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1073 - mean_squared_error: 0.0146 - val_loss: 0.1084 - val_mean_squared_error: 0.0148 Epoch 5/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1074 - mean_squared_error: 0.0145 - val_loss: 0.1084 - val_mean_squared_error: 0.0148 Epoch 6/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 6ms/step - loss: 0.1071 - mean_squared_error: 0.0144 - val_loss: 0.1067 - val_mean_squared_error: 0.0142 Epoch 7/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1051 - mean_squared_error: 0.0139 - val_loss: 0.1049 - val_mean_squared_error: 0.0137 Epoch 8/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1044 - mean_squared_error: 0.0136 - val_loss: 0.1047 - val_mean_squared_error: 0.0136 Epoch 9/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1042 - mean_squared_error: 0.0136 - val_loss: 0.1044 - val_mean_squared_error: 0.0135 Epoch 10/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1037 - mean_squared_error: 0.0134 - val_loss: 0.1044 - val_mean_squared_error: 0.0135 Epoch 11/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1038 - mean_squared_error: 0.0134 - val_loss: 0.1041 - val_mean_squared_error: 0.0134 Epoch 12/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1034 - mean_squared_error: 0.0134 - val_loss: 0.1042 - val_mean_squared_error: 0.0135 Epoch 13/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1034 - mean_squared_error: 0.0133 - val_loss: 0.1039 - val_mean_squared_error: 0.0134 Epoch 14/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1037 - mean_squared_error: 0.0134 - val_loss: 0.1038 - val_mean_squared_error: 0.0134 Epoch 15/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1033 - mean_squared_error: 0.0133 - val_loss: 0.1040 - val_mean_squared_error: 0.0134 Epoch 16/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1036 - mean_squared_error: 0.0134 - val_loss: 0.1040 - val_mean_squared_error: 0.0135 Epoch 17/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1032 - mean_squared_error: 0.0133 - val_loss: 0.1039 - val_mean_squared_error: 0.0134 Epoch 18/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1032 - mean_squared_error: 0.0133 - val_loss: 0.1036 - val_mean_squared_error: 0.0133 Epoch 19/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1032 - mean_squared_error: 0.0133 - val_loss: 0.1036 - val_mean_squared_error: 0.0133 Epoch 20/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1032 - mean_squared_error: 0.0133 - val_loss: 0.1043 - val_mean_squared_error: 0.0136 Epoch 21/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1033 - mean_squared_error: 0.0133 - val_loss: 0.1035 - val_mean_squared_error: 0.0133 Epoch 22/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1033 - mean_squared_error: 0.0133 - val_loss: 0.1038 - val_mean_squared_error: 0.0134 Epoch 23/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1033 - mean_squared_error: 0.0133 - val_loss: 0.1041 - val_mean_squared_error: 0.0135 Epoch 24/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 10s 6ms/step - loss: 0.1030 - mean_squared_error: 0.0132 - val_loss: 0.1052 - val_mean_squared_error: 0.0139 Epoch 25/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1031 - mean_squared_error: 0.0132 - val_loss: 0.1034 - val_mean_squared_error: 0.0132 Epoch 26/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1031 - mean_squared_error: 0.0132 - val_loss: 0.1036 - val_mean_squared_error: 0.0133 Epoch 27/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1031 - mean_squared_error: 0.0132 - val_loss: 0.1034 - val_mean_squared_error: 0.0133 Epoch 28/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1029 - mean_squared_error: 0.0132 - val_loss: 0.1036 - val_mean_squared_error: 0.0133 Epoch 29/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1031 - mean_squared_error: 0.0132 - val_loss: 0.1034 - val_mean_squared_error: 0.0133 Epoch 30/30 1688/1688 ━━━━━━━━━━━━━━━━━━━━ 9s 5ms/step - loss: 0.1029 - mean_squared_error: 0.0132 - val_loss: 0.1035 - val_mean_squared_error: 0.0133
